Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics PDF full book. Access full book title Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics by National Aeronautics and Space Adm Nasa. Download full books in PDF and EPUB format.
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781729362686
Category : Science
Languages : en
Pages : 54
Get Book Here
Book Description
Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation. Farassat, F. Langley Research Center...
Author: F. Farassat
Publisher:
ISBN:
Category : Aerodynamics
Languages : en
Pages : 60
Get Book Here
Book Description
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781729362686
Category : Science
Languages : en
Pages : 54
Get Book Here
Book Description
Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation. Farassat, F. Langley Research Center...
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 364
Get Book Here
Book Description
Author: Houbing Song
Publisher: John Wiley & Sons
ISBN: 1119226430
Category : Technology & Engineering
Languages : en
Pages : 872
Get Book Here
Book Description
Provides the foundations and principles needed for addressing the various challenges of developing smart cities Smart cities are emerging as a priority for research and development across the world. They open up significant opportunities in several areas, such as economic growth, health, wellness, energy efficiency, and transportation, to promote the sustainable development of cities. This book provides the basics of smart cities, and it examines the possible future trends of this technology. Smart Cities: Foundations, Principles, and Applications provides a systems science perspective in presenting the foundations and principles that span multiple disciplines for the development of smart cities. Divided into three parts—foundations, principles, and applications—Smart Cities addresses the various challenges and opportunities of creating smart cities and all that they have to offer. It also covers smart city theory modeling and simulation, and examines case studies of existing smart cities from all around the world. In addition, the book: Addresses how to develop a smart city and how to present the state of the art and practice of them all over the world Focuses on the foundations and principles needed for advancing the science, engineering, and technology of smart cities—including system design, system verification, real-time control and adaptation, Internet of Things, and test beds Covers applications of smart cities as they relate to smart transportation/connected vehicle (CV) and Intelligent Transportation Systems (ITS) for improved mobility, safety, and environmental protection Smart Cities: Foundations, Principles, and Applications is a welcome reference for the many researchers and professionals working on the development of smart cities and smart city-related industries.
Author: Victor Kowalenko
Publisher: Academic Press
ISBN: 0128045116
Category : Mathematics
Languages : en
Pages : 314
Get Book Here
Book Description
The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics. - Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers - Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches - Describes how to program the partition method for a power series expansion and the BRCP algorithm
Author: Wuhong Wang
Publisher: Springer Nature
ISBN: 9811654298
Category : Technology & Engineering
Languages : en
Pages : 841
Get Book Here
Book Description
These proceedings gather selected papers from the 11th International Conference on Green Intelligent Transportation Systems and Safety, held in Beijing, China on October 17-19, 2020. The book features cutting-edge studies on Green Intelligent Mobility Systems, the guiding motto being to achieve “green, intelligent, and safe transportation systems”. The contributions presented here can help promote the development of green mobility and intelligent transportation technologies to improve interconnectivity, resource sharing, flexibility and efficiency. Given its scope, the book will benefit researchers and engineers in the fields of Transportation Technology and Traffic Engineering, Automotive and Mechanical Engineering, Industrial and System Engineering, and Electrical Engineering alike. The readers will be able to find out the Advances in Green Intelligent Transportation System and Safety.
Author: Ram P. Kanwal
Publisher: Springer Science & Business Media
ISBN: 1468400355
Category : Mathematics
Languages : en
Pages : 474
Get Book Here
Book Description
This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.
Author: Marco G. Beghi
Publisher: BoD – Books on Demand
ISBN: 9533075724
Category : Technology & Engineering
Languages : en
Pages : 670
Get Book Here
Book Description
The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis.
Author: John E Ffowcs Williams
Publisher: World Scientific
ISBN: 9814551724
Category :
Languages : en
Pages : 1028
Get Book Here
Book Description
This conference provided a forum for active researchers to discuss the state of the art in theoretical and computational acoustics. Topics covered structural acoustics, scattering, 3-dimensional propagational problems, fluid/elastic interfaces, wavelets and their impact on acoustics, computational methods and supercomputing.
Author: Matthew C. M. Wright
Publisher: World Scientific
ISBN: 1860944965
Category : Science
Languages : en
Pages : 310
Get Book Here
Book Description
Based on lectures given at a one week summer school held at the University of Southampton, July 2003.
